Water reservoir

A water reservoir is filled through one inlet 4 hours longer than through both inlets, and through another inlet 9 hours longer. How long does each inlet take to fill it separately?

Final Answer:

a =  10 h
b =  15 h

Step-by-step explanation:

$$\begin{gathered} \frac{1}{a}+\frac{1}{b}=\frac{1}{s} \\ s=\frac{ab}{a+b} \\ a=4+s \\ b=9+s \\ s(a+b)=ab \\ s(4+s+9+s)=(4+s)(9+s) \\ {s}^2=36 \\ s=\sqrt{36}=6\text{h} \\ a=4+s=4+6=10\text{h} \end{gathered}$$

$b=9+s=9+6=15\text{h}$

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